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Calc wk1 HW

This document provides homework questions from calculus chapters on inverse trigonometric functions, tangent and velocity problems, and limits of functions. It lists learning objectives for each section and provides 4 problems per section for students to practice. It directs students to additional optional practice problems in the free online textbook. The purpose is for students to work through these essential problems before their next tutorial.

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Abdullah Mustafa
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42 views4 pages

Calc wk1 HW

This document provides homework questions from calculus chapters on inverse trigonometric functions, tangent and velocity problems, and limits of functions. It lists learning objectives for each section and provides 4 problems per section for students to practice. It directs students to additional optional practice problems in the free online textbook. The purpose is for students to work through these essential problems before their next tutorial.

Uploaded by

Abdullah Mustafa
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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HONOUR HOMEWORK

[Source: “Calculus Early Transcendentals” by James Stewart, 8th ed., 2015]

The following questions are NOT to be handed in, but it is essential to try them
before tutorial!

 The questions with a red star are the “at least do these for now/start with these” absolute bare-
minimum questions during the occasional super-busy week.

1.4: INVERSE TRIGONOMETRIC FUNCTIONS (part of Inverse Functions


section)

Learning Objectives:

 Have an understanding of inverse trigonometric functions and how to perform


basic associated calculations;
 Importance of the ranges of the inverse trigonometric functions;
 Derivations involving inverse trigonometric functions.

1) Find the exact value of the expression csc √2

2) Prove that cos (sin ) = √1 −

3) Simplify the expression sin (tan )

4) Find the domain and range of the function ( ) = sin (3 + 1)

Need additional practice? Try the following ODD numbered questions in 1.4 of our
free online textbook: # 207 – 215 and 221 – 228.
2.1: THE TANGENT AND VELOCITY PROBLEMS (part of A Preview of
Calculus)

Learning Objectives:

 Estimation of tangents to the graph of a function, slope and equation of tangent


line.

1) If a ball is thrown into the air with a velocity of 40 ft/s, its height in feet seconds later is
given by = 40 − 16 .

a) Find the average velocity for the time period beginning when = 2 and lasting
i) 0.5 seconds ii) 0.1 seconds
iii) 0.05 seconds iv) 0.01 seconds

b) Estimate the instantaneous velocity when = 2.

Need additional practice? Try the following ODD numbered questions in 2.1 of our
free online textbook: # 16 – 23.
2.2: THE LIMIT OF A FUNCTION

Learning Objectives:

 Definition of the (sided) limit of a function at a point;


 Infinite limits, vertical asymptotes.

1) For the function whose graph is given, state the value of each quantity, if exists. If it
does not exist, explain why.
a) lim! ( ) b) lim" ( ) c) lim ( )
→ → →

d) lim! ( ) e) lim" ( ) f) lim ( )


→ → →

g) (2) h) lim ( )
→#

2) For the function $ whose graph is shown below, state the following.

a) lim $( ) b) lim $( ) c) lim $( )


%→ & %→ ' %→

d) lim! $( ) e) lim $( )
%→ ( %→ ("

f) The equation of the vertical asymptotes.


3) Sketch the graph of an example of function $ that satisfies all of the given conditions.
lim" $( ) = 4, lim! $( ) = 2, lim $( ) = 2,
%→' %→' %→

$(3) = 3, $(−2) = 1
%+
4) Determine the infinite limit lim" %
%→* *

Need additional practice? Try the following ODD numbered questions in 2.2 of our
free online textbook: #30-82 are all doable.

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